What is a cube root formula?

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Quick Answer

To find the cube root of a number, find all of the number’s prime factors. A cube root is a number that, when cubed, gives the original number. If there are exactly three prime factors that are all the same, the number is a perfect cube.

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The cube root of 8 is 2, because 2 * 2 * 2 = 8. Eight is referred to as a "perfect cube" because its cube root is a whole number. For example, to find the cube root of 125, find its prime factors. Since 125 = 5 * 5 * 5, the cube root of 125 is 5.

If the number does not have exactly three equal prime factors, the cube root can only be expressed as an irrational number. So, the cube root of 15 is simply cube root 15.

If the number has three equal prime factors plus other prime factors, it is also an irrational number. For example, to find the cube root of 375, find its prime factors. 325 = 5 * 5 * 5 * 3. So the cube root of 375 is 5 cube root 3.

Remember that the cube of a number is the number multiplied by itself three times. So the cube root is the number that, when multiplied by itself three times, gives the initial number. Since 2 * 2 * 2 is 8, 2 cubed is 8, and the cube root of 8 is 2.